For illustration we choose \(\lambda _{22}=0.18\)  and \(\lambda _{11}=0.2\)  which correspond to dimensionless couplings of conventional \(s\) -wave superconductors [1]}. Usually in two-band systems we have [2]} \(\lambda _{12} \ll \lambda _{11},\lambda _{22}\) . Here we consider \(\lambda _{12}=0.005,0.01\)  and \(0.02\) . The ratio of the band DOSs \(N_2/N_1\)  is close to 1 in most cases [3]}, and below we set \(N_2/N_1=1\) . Finally, \(\tilde{\mu }\) , \(\tilde{\varepsilon }\) , and \(m_2/m_1\)  can change significantly from one material to another, depending on fabrication details and doping, and we treat these quantities as free parameters.
